JEE Main 2021 · MathsNumerical answerNumerical valueHardCalculation

JEE Main 27 August 2021, Shift 1, Maths Q90

Question 90 of 90 in this shift, Maths question 30 of 30, Section B.

\int\frac{dx}{(x^2+x+1)^2}=a\tan^{-1}\left(\frac{2x+1}{\sqrt{3}}\right)+b\left(\frac{2x+1}{x^2+x+1}\right)+C

x>0

where C is the constant of integration, then the value of

9(\sqrt{3}a+b)

is equal to __________.

Official answer

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Tangent Trigonometric Substitution

Same topic in other shifts

All Integration by Substitution questions

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3 Apr 2025, Shift 1 · Q18Let $f(x) = \int x^3\sqrt{3 - x^2}\,dx$ . If $5f(\sqrt{2}) = -4$ , then $f(1)$ is equal toMediumSingle correct
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5 Apr 2024, Shift 1 · Q11The integral $\int_0^{\pi/4}\frac{136\sin x}{3\sin x+5\cos x}\,dx$ is equal to :MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.